The present invention generally relates to image formation, and more particularly, to a color image forming apparatus such as a color printer for printing out color images, color copying apparatus and the like, and especially, to a full color image forming apparatus capable of effecting favorable color reproduction.
In the color image forming apparatus such as a color printer, color copying apparatus or the like as referred to above, based on a principle of subtractive color mixture employing inks for cyan, magenta and yellow which are the complementary colors respectively of red, green, and blue of three primary colors for color light, it is an object for color reproduction to achieve colors equal to target colors for the respective color image forming apparatuses in a CRT (cathode ray tube), color original documents, etc.
However, inks actually available have a spectral characteristic which is too broad to act as an ideal absorbing filter with respect to respective color lights. By way of example, the spectral absorbing characteristics of the subliming dye generally employed are shown in FIGS. 7(a) to 7(c), from which it is seen that the spectral absorbing characteristics of the inks actually present or available are excessively broad, and as represented by hatched portions in FIGS. 7(a) to 7(c), there are present so-called unnecessary absorbing components which absorb even color lights having wavelengths to be normally transmitted completely, and thus, density different from that to be reproduced by each ink is reproduced during color mixing, thereby giving rise to color turbidity through reduction of chroma or saturation.
Additionally, in order to achieve the color equal to the target color, there is a problem related to deviation between the central wavelength of the spectral absorbing characteristic of the ink and the central wavelength of the spectral characteristic of the fluorescent material for the CRT (cathode ray tube-referred to as CRT hereinafter) or the central wavelength of the spectral characteristic of a color filter for a color scanner.
For example, the spectral characteristics for the fluorescent materials of a typical CRT are shown in FIG. 8, from which it is observed that the central wavelength of the spectral characteristic for the fluorescent material in each color is not in agreement with that of the spectral absorbing characteristic of the ink referred to earlier in FIG. 7. From the above fact, it will be understood that, even if the color turbidity due to the unnecessary absorbing component of the ink is prevented, if there is a deviation between the central wavelength of the spectral absorbing characteristic for the ink and the central wavelength of the spectral characteristic for each fluorescent material of the CRT or the central wavelength of the spectral characteristic of the color separation filter, hue of the color to be reproduced undesirably becomes different from the target color.
With respect to the problem as referred to above, a correcting method referred to as masking has conventionally been employed mainly with respect to the field of printing.
The practice most commonly employed is that called "linear masking" and represented by an equation (1) given below. ##EQU1##
The linear masking is arranged to determine the ink density signals (C,M,Y) for controlling the density of inks to be employed, by the linear matrix calculation of three primary color density signals (D.sub.R, D.sub.G, D.sub.B) which are complementary colors to the three primary color luminance signals (R,G,B) as represented by the above equation (1).
The linear masking is based on the assumption that, in the subtractive color mixture employing actual inks, the additive law of density (Lambert-Beer law) and proportional law may be established, but in the color reproduction employing the actual inks, there exist various non-linear factors such as re-subliming phenomenon of inks, internal reflection of inks, etc., for example, in the case of the subliming type thermal transfer recording system, and in the strict sense, the additive law and proportional law as referred to above can not be established.
Accordingly, a non-linear type higher order masking which determines the ink density signals (C,M,Y) by polynomials of higher order with respect to the three primary color density signals (D.sub.R, D.sub.G, D.sub.B) has been proposed, among which the simplest quadratic masking equations are given below as equations (2). ##EQU2##
By the above representation, the non-linearity existing in the color reproduction employing the actual inks is approximated by the quadratic equations.
Meanwhile, there has also conventionally been proposed in Japanese Patent Laid-Open Publication Tokkaisho No. 62-72277, a method in which the spectral characteristic of a color separation system (scanner) for reading the original image is corrected by matrix calculation, and the signals thereof are subjected to complementary color conversion, with further application of the linear masking thereto, for conversion into ink density signals to obtain color hard copy.
The above method is arranged to subject the color image signals (R0,G0,B0) obtained by reading the original image, to the matrix calculation as shown in an equation (3) given below, and further, to complementary color conversion, and then, the linear masking is applied for conversion into the ink density signals (D.sub.C,D.sub.M,D.sub.Y) so as to obtain the color hard copy. ##EQU3##
Subsequently, the conventional method of determining correction factors to be employed for the linear masking, non-linear higher order masking, etc. will be explained with reference to FIG. 9.
It is difficult to analytically determine nine correction factors {a k1} (k=1.about.3, 1=1.about.3) used for such linear masking, twenty-seven correction factors a0 to a26 adopted for the quadratic masking, and {a k1} {S k1} (k=1.about.3,1=1.about.3) used for the equation (3), and they are conventionally determined by the method of least squares with respect to the density signals.
The method as referred to above will be more specifically explained with reference to FIG. 9, which shows a model for the color reproduction system employing such a method. In FIG. 9, X represents the density signal already known, and color chips are prepared by a recording system dealt with by the color modification (color correction) through employment of a sufficiently large number (n pieces) of X. The color chips thus prepared are subjected to color separation by a scanner (three color separating system), and the three primary color density signals D are obtained. When a transfer function of the above recording/reproducing system is represented by .phi., the color correction system is imparted with a reverse characteristic thereof, and a value .phi..sup.-1 is determined so that the signal X" after passing through the color correction system and the original signal X are reduced to minimum on the average. In other words, the color correction factor is determined by the converging calculation employing the computer so as to minimize the errors related to the density signals between the density signal X used for the preparation of the color chips and the density signal X' for the output of the color modification system.
Such practice as above is described, for example, in an article "Image processing for color reproduction", a separate volume of a magazine "Shashin Kogyo" (Photographic Industry) entitled "Imaging Part 1".
However, in the conventional color correction techniques such as the linear masking, non-linear higher order masking, etc., it is intended to effect the correction by the calculation with respect to the density signals of subtractive color mixture, including color turbidity by the unnecessary absorbing component of the actual inks and the deviation in hue due to deviation between the central wavelength of the spectral absorbing characteristic of the ink and the central wavelength of the spectral characteristic of the fluorescent material for the CRT or the central wavelength of the spectral characteristic of a color filter for the color scanner.
Particularly, in the liner masking, the non-linearity factor as described earlier is also approximated by the linear calculation, and the correcting accuracy thereof is considered to be insufficient for the use in which color highly faithful color reproduction is required.
Moreover, the non-linear higher order masking is not intended to express the color reproduction of recording system analytically, but to approximate the non-linearity of the color reproduction through addition of the non-linear item and also, to effect the correction only by the calculation with respect to the density signals, and therefore, there is such a problem that the correcting accuracy thereof is still insufficient.
Meanwhile, in the method as disclosed in Japanese Patent Laid-Open Publication Tokkaisho No. 62-72277, it is so arranged to correct the spectral characteristic of the color separating system (scanner) by the matrix calculation for conversion into the density signals by the complementary color conversion, thereby to correct the spectral characteristic of the ink by the linear masking in the density signals. In other words, the correction with respect to the spectral characteristic of the ink is of the conventional linear masking, and therefore, the correcting accuracy was not sufficient, either.
On the other hand, the conventional correction factor determining method which minimizes the errors related to the density signals is superior in that the determination may be made by the converging calculation employing the computer. However, the correction factor as obtained by the conventional correction factor determining method is to effect the correction including not only the spectral absorbing characteristic of the ink, but also the spectral distribution characteristic of the color filter for the scanner (three color separation system), and thus, there is such a problem that the method can not be applied to the determination of the correction factor in the apparatus without any scanner, and as a video printer for printing out the color image to be outputted to the CRT, etc.
Moreover, the conventional correction factor determining method is intended to minimize the errors related to the density signals, with the density signals being set as evaluation values, and is not arranged to minimize the difference of colors perceived by man. From the above fact, there has been such a problem that the correction factor as determined by the conventional correction factor determining method is not most suitable from the viewpoint of color reproduction.